Can machine learning accelerate soft material parameter identification from complex mechanical test data?

Mechanical properties of fresh rhesus monkey brain tissue

Studying brain tissue mechanics is critical for understanding how the brain's physical properties influence its biological functions. Non-human primates, such as rhesus monkeys, are a key translational model for human neuroscience research, yet their brain tissue mechanics remain poorly understood. We report the mechanical properties of rhesus monkey white (corona radiata, CR) and gray (basal ganglia, BG) matter during compression relaxation, tension relaxation, tension-compression cycling (strain = 0.15, nCR = 21, nBG = 14), and shear cycling (strain = 0.3, nCR = 17, nBG = 9). Compression relaxation yields short and long-term time constants of 1.13 ± 0.041 s and 26.3 ± 0.68 s for CR and 1.22 ± 0.046 s and 28.3 ± 0.70 s for BG. Tension relaxation yields short and long-term time constants of 1.10 ± 0.052 s and 28.2 ± 0.82 s for CR and 1.19 ± 0.052 s and 29 ± 1.3 s for BG. Tension-compression cycling yields elastic moduli (E₁, E₂, E₃) of 36 ± 3.8 kPa, 0.61 ± 0.096 kPa, and 9.3 ± 0.90 kPa for CR and 27 ± 4.8 kPa, 0.68 ± 0.092 kPa, and 8 ± 1.0 kPa for BG. Shear cycling yields E₁, E₂, and E₃ of 3.9 ± 0.77 kPa, 0.19 ± 0.034 kPa, and 3.1 ± 0.40 kPa for CR and 2.8 ± 0.52 kPa, 0.18 ± 0.058 kPa, and 3.2 ± 0.53 kPa for BG. Hysteresis areas are also captured during tension-compression and shear cycling. These findings extend the translatability of rhesus monkey models for neuroscience. STATEMENT OF SIGNIFICANCE: While rhesus monkeys are a valuable translational model in human neuroscience research, there is a huge gap in knowledge about rhesus monkey brain tissue mechanics. This study serves to increase our understanding of rhesus monkey brain tissue mechanics and is the first to report the stiffness, time constant, and hysteresis parameters for rhesus monkey brain tissue in compression, tension, and shear for both the corona radiata and basal ganglia. The data is available in an open-source format, allowing others to fit and validate their mechanical models.

Development and calibration of digital twins for human skin growth in tissue expansion

Tissue expansion (TE), an essential technique in reconstructive surgery, leverages the growth of skin in response to stretch. However, human skin growth dynamics have not been evaluated in vivo. Previously, we quantified this process in a porcine model and developed a calibrated computational framework. Here, we create patient-specific finite element (FE) models of skin growth in TE using longitudinal 3D photos collected during TE treatment. These geometries enable Bayesian model calibration, accounting for uncertainties in boundary conditions, mechanical properties, and biological parameters. The framework incorporates prior knowledge from the porcine model as well as literature information on human skin mechanics. The likelihood function assesses alignment between predicted and observed geometries, and predicted and observed skin growth. To efficiently sample the posterior distribution, we use Markov Chain Monte Carlo (MCMC) with Gaussian process surrogates, reducing computational cost. This pipeline is demonstrated in five TE cases. Post-calibration, FE models closely match 3D photos, with errors below 2 mm on average. Notably, Bayesian calibration collapses the critical stretch parameter posterior distribution. This study presents the first in vivo measurement of human skin growth, confirming that FE models accurately capture TE in the clinical setting, and that porcine-derived parameters provide a strong prior for Bayesian calibration in the clinical case. These findings support the development of personalized digital twins for TE, enhancing surgical planning and outcomes. Statement of significance Tissue expansion (TE) is widely used in reconstructive surgery, particularly for breast reconstruction and pediatric defect repair. While skin growth has been quantified in animal models, this work provides the first clinical measurement of human skin growth during TE. We employ a Bayesian calibration framework to create personalized finite element (FE) simulations for five TE cases. The initial FE model is constructed from a patient's 3D photo taken at the start of treatment. Then, uncertainties in mechanical and biological parameters as well as boundary conditions are sampled and the model run. We use Gaussian process surrogates to replace the FE model. Calibration of parameters is done with 3D photos taken longitudinally during TE. This pipeline for skin digital twins can enhance personalized TE procedures, optimizing outcomes and reducing complications.

FEBio FINESSE: An Open-Source Finite Element Simulation Approach to Estimate In Vivo Heart Valve Strains Using Shape Enforcement

PURPOSE

Finite element simulations are an enticing tool to evaluate heart valve function; however, patient-specific simulations derived from 3D echocardiography are hampered by several technical challenges. The objective of this work is to develop an open-source method to enforce matching between finite element simulations and in vivo image-derived heart valve geometry in the absence of patient-specific material properties, leaflet thickness, and chordae tendineae structures.

METHODS

We evaluate FEBio Finite Element Simulations with Shape Enforcement (FINESSE) using three synthetic test cases considering a range of model complexity. FINESSE is then used to estimate the in vivo valve behavior and leaflet strains for three pediatric patients.

RESULTS

Our results suggest that FINESSE can be used to enforce finite element simulations to match an image-derived surface and estimate the first principal leaflet strains within ± 0.03 strain. Key considerations include: (i) defining the user-defined penalty, (ii) omitting the leaflet commissures to improve simulation convergence, and (iii) emulating the chordae tendineae behavior via prescribed leaflet free edge motion or a chordae emulating force. In all patient-specific cases, FINESSE matched the target surface with median errors of approximately the smallest voxel dimension. Further analysis revealed valve-specific findings, such as the tricuspid valve leaflet strains of a 2-day old patient with HLHS being larger than those of two 13-year old patients.

CONCLUSIONS

FEBio FINESSE can be used to estimate patient-specific in vivo heart valve leaflet strains. The development of this open-source pipeline will enable future studies to begin linking in vivo leaflet mechanics with patient outcomes.

Simulation and Analysis of the Loading, Relaxation, and Recovery Behavior of Polyethylene and Its Pipes

Spring-dashpot models have long been used to simulate the mechanical behavior of polymers, but their usefulness is limited because multiple model parameter values can reproduce the experimental data. In view of this limitation, this study explores the possibility of improving uniqueness of parameter values so that the parameters can be used to establish the relationship between deformation and microstructural changes. An approach was developed based on stress during the loading, relaxation, and recovery of polyethylene. In total, 1000 sets of parameter values were determined for fitting the data from the relaxation stages with a discrepancy within 0.08 MPa. Despite a small discrepancy, the 1000 sets showed a wide range of variation, but one model parameter, σv,L0, followed two distinct paths rather than random distribution. The five selected sets of parameter values with discrepancies below 0.04 MPa were found to be highly consistent, except for the characteristic relaxation time. Therefore, this study concludes that the uniqueness of model parameter values can be improved to characterize the mechanical behavior of polyethylene. This approach then determined the quasi-static stress of four polyethylene pipes, which showed that these pipes had very close quasi-static stress. This indicates that the uniqueness of the parameter values can be improved for the spring-dashpot model, enabling further study using spring-dashpot models to characterize polyethylene's microstructural changes during deformation.

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue

Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the "most rewarding" training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.

Automated model discovery for human brain using Constitutive Artificial Neural Networks

The brain is our softest and most vulnerable organ, and understanding its physics is a challenging but significant task. Throughout the past decade, numerous competing models have emerged to characterize its response to mechanical loading. However, selecting the best constitutive model remains a heuristic process that strongly depends on user experience and personal preference. Here we challenge the conventional wisdom to first select a constitutive model and then fit its parameters to data. Instead, we propose a new strategy that simultaneously discovers both model and parameters. We integrate more than a century of knowledge in thermodynamics and state-of-the-art machine learning to build a Constitutive Artificial Neural Network that enables automated model discovery. Our design paradigm is to reverse engineer the network from a set of functional building blocks that are, by design, a generalization of popular constitutive models, including the neo Hookean, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models. By constraining input, output, activation functions, and architecture, our network a priori satisfies thermodynamic consistency, objectivity, symmetry, and polyconvexity. We demonstrate that-out of more than 4000 models-our network autonomously discovers the model and parameters that best characterize the behavior of human gray and white matter under tension, compression, and shear. Importantly, our network weights translate naturally into physically meaningful parameters, such as shear moduli of 1.82kPa, 0.88kPa, 0.94kPa, and 0.54kPa for the cortex, basal ganglia, corona radiata, and corpus callosum. Our results suggest that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in soft tissue modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. STATEMENT OF SIGNIFICANCE: Human brain is ultrasoft, difficult to test, and challenging to model. Numerous competing constitutive models exist, but selecting the best model remains a matter of personal preference. Here we automate the process of model selection. We formulate the problem of autonomous model discovery as a neural network and capitalize on the powerful optimizers in deep learning. However, rather than using a conventional neural network, we reverse engineer our own Constitutive Artificial Neural Network from a set of modular building blocks, which we rationalize from common constitutive models. When trained with tension, compression, and shear experiments of gray and white matter, our network simultaneously discovers both model and parameters that describes the data better than any existing invariant-based model. Our network could induce a paradigm shift from user-defined model selection to automated model discovery.